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Understanding Linear Equations

Total questions: 10

Worksheet time: 5mins

Name
Class
Date
1.

Solve the system of equations: 2x + 3y = 12 and x - y = 1.

a)

(3, 2)

b)

(4, 0)

c)

(1, 4)

d)

(2, 3)

2.

What is the solution to the equations: 3x + 4y = 24 and 2x - y = 3?

a)

(36/11, 39/11)

b)

(12, 6)

c)

(0, 0)

d)

(5, 5)

3.

Using substitution, solve for y in the equations: y = 2x + 1 and 3x + 2y = 12.

a)

y = 27/7

b)

y = 3x + 2

c)

y = 4x + 3

d)

y = 5x - 1

4.

Apply the elimination method to find x and y in: 4x + 5y = 20 and 2x - 3y = 6.

a)

x = 10, y = 0

b)

x = 45/11, y = 8/11

c)

x = 5, y = 2

d)

x = 0, y = 4

5.

If x + y = 10 and x - y = 2, what are the values of x and y?

a)

x = 6, y = 4

b)

x = 4, y = 6

c)

x = 8, y = 2

d)

x = 5, y = 5

6.

A store sells pencils for $0.50 each and erasers for $0.75 each. If you buy 10 items for $6.00, how many of each did you buy?

a)

5 pencils and 5 erasers

b)

7 pencils and 3 erasers

c)

4 pencils and 6 erasers

d)

6 pencils and 4 erasers

7.

Solve the following system using substitution: y = 3x - 4 and 2x + y = 10.

a)

(5, 5)

b)

(14/5, 22/5)

c)

(2, 2)

d)

(0, 10)

8.

Using elimination, find the values of x and y in: 5x + 2y = 30 and 3x + 4y = 24.

a)

x = 6, y = 3

b)

x = 4, y = 8

c)

x = 2, y = 10

d)

x = 5.14, y = 2.15

9.

If the sum of two numbers is 15 and their difference is 3, what are the two numbers?

a)

8 and 7

b)

10 and 5

c)

12 and 3

d)

The two numbers are 9 and 6.

10.

A farmer has chickens and cows. If he has 20 animals in total and there are 56 legs, how many chickens and cows does he have?

a)

12 chickens and 8 cows

b)

8 chickens and 12 cows

c)

10 chickens and 10 cows

d)

14 chickens and 6 cows